Evaluation of false discovery rate and power via sample size in microarray studies

Abstract

Microarray studies are now common for human, agricultural plant and animal studies. False discovery rate (FDR) is widely used in the analysis of large-scale microarray data to account for problems associated with multiple testing. A well-designed microarray study should have adequate statistical power to detect the differentially expressed (DE) genes, while keeping the FDR acceptably low. In this paper, we used a mixture model of expression responses involving DE genes and non-DE genes to analyse theoretical FDR and power for simple scenarios where it is assumed that each gene has equal error variance and the gene effects are independent. A simulation study was used to evaluate the empirical FDR and power for more complex scenarios with unequal error variance and gene dependence. Based on this approach, we present a general guide for sample size requirement at the experimental design stage for prospective microarray studies. This paper presented an approach to explicitly connect the sample size with FDR and power. While the methods have been developed in the context of one-sample microarray studies, they are readily applicable to two-sample, and could be adapted to multiple-sample studies.

Keywords:

• microarray
• false discovery rate
• power
• multiple testing
• mixture model

Acknowledgements

We are grateful to Mehar Khatkar and Peter Williamson for their valuable advice. The work reported here was supported with funds from the Co-operative Research Centre for Innovative Dairy Products. J.S. was the recipient of a University of Sydney Postgraduate Award scholarship. We thank the reviewers for their helpful comments.